The 19-year-old remains without a first-team appearance for the Premier League club, but the youngster played an active role with the senior squad during pre-season.
That has resulted in the Merseyside giants offering improved terms to the stopper, who admits that he jumped at the opportunity to extend his stay.
Kelleher told the club's official website: "I'm very happy to sign a long deal with the club. I'm really enjoying my football here so I was happy to sign. Once the deal came in and I was happy, it was an easy decision really.
"I've been doing the same things but getting better every day. Training at Melwood, you improve much more. Alisson and Simon [Mignolet] and Kamil [Grabara] are here and we train to the highest level every day."